Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories

Details Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories

2011-11-17

arxiv.org/abs/1111.4003v2

Mathematics

K-Theory and Homology

67 pages. Added table of contents

Scientific paper

We prove a conjecture of Hesselholt and Ausoni-Rognes, establishing localization cofiber sequences of spectra for THH(ku) and TC(ku). These sequences support Hesselholt's view of the map l to ku as a "tamely ramified" extension of ring spectra, and validate the hypotheses necessary for Ausoni's simplified computation of V(1)_* K(KU). In order to make sense of the relative term THH(ku|KU) in the cofiber sequence and prove these results, we develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. We resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized devissage theorem.

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